Question

Brainliest to correct answer

Answer 1

Question 1:

For this case we must factor the following expression:

$n ^ 2 + 2n-24 = 0$

We must find two numbers that when multiplied result in -24 and when added together result in 2. These numbers are: 6 and -4.

$6*(-4)=-24\\6-4=2$

Thus, we factor:

$(x + 6) (x-4) = 0$

The roots are:

$x_ {1} = - 6\\x_ {2} = 4$

Answer:

Option C

Question 2:

For this case we have that by definition, the area of a rectangle is given by:

$A = w * l$

Where:

w: Is the width of the rectangle

l: is the length of the rectangle

According to the statement we have:

$A = 30 \ ft ^ 2\\l = 3w-1$

Substituting:

$(3w-1) w = 30\\3w ^ 2-w = 30\\3w ^ 2-w-30 = 0$

Where:

$a = 3\\b = -1\\c = -30$

The solution:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}\\x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (3) (- 30)}} {2 (3)}\\x = \frac {1 \pm \sqrt {1 + 360}} {2 (3)}\\x = \frac {1 \pm \sqrt {361}} {6}\\x = \frac {1\pm19} {6}$

We have two roots:

$x_ {1} = \frac {1-19} {6} = \frac {-18} {6} = - 3\\x_ {2} = \frac {1 + 19} {6} =\frac {20} {6} = 3,333$

We choose the second value (the positive), when rounding is $3.33 \ ft$

Answer:

Option A